Cross Correlation of Omnidirectional, Broadband Signals Scattered by a Random Pressure-Release Surface

Expressions for the cross correlation of omnidirectional, broadband continuous-wave (CW) acoustic signals scattered by a pressure-release random surface are derived for both vertically and horizontally spaced hydrophones using the Kirchhoff approximation for the boundary values and the Fresnel phase approximation. The resulting expressions for the spatial coherence are simple in form and require no approximations in the description of the random surface. As the surface becomes perfectly smooth, the expressions reduce to the image solution, thus ensuring the proper limiting behavior. Two narrowband models for vertical coherence were compared to experimental data collected during a sea test at the frequencies of 14, 16, 18, and 20 kHz with a maximum hydrophone spacing of 1.4 m. One model used the measured sound-speed profile (SSP) to estimate input parameters, and the other model assumed isospeed conditions. The agreement between the experimental data and the model based on the measured SSP is very good, and the agreement with the isospeed model is almost as good.